method is relatively old but it has been dramatically improved in the last decades. This method divides into three steps. First an upper bound on the number of solutions is computed. This bound has to be as sharp as possible. Therefore, it is computed by, at least, four different methods and the best value, say , is kept. In the second step, a system of polynomial equations is generated which has exactly solutions that are easy to compute. This new system has the same number of variables and the same number of equations and the same general structure as the system to solve, . Then a homotopy between the two systems is considered. It consists, for example, of the straight line between the two systems, but other paths may be considered, in particular to avoid some singularities, in the system . The homotopy continuation consists in deforming the parameter from 0 to 1 and following the solutions during this deformation. This gives the desired solutions for . Following means that, if , the solutions for are deduced from the solutions for by Newton's method. The difficulty here is to well choose the value of Too large, Newton's convergence may be slow and may even jump from a solution path to another one. Too small, and the number of steps slows down the method. Numerically solving from the rational univariate representation To deduce the numeric values of the solutions from a RUR seems easy: it suffices to compute the roots of the univariate polynomial and to substitute them in the other equations. This is not so easy because the evaluation of a polynomial at the roots of another polynomial is highly unstable. The roots of the univariate polynomial have thus to be computed at a high precision which may not be defined once for all. There are two algorithms which fulfill this requirement. Aberth method, implemented in MPSolve computes all the complex roots to any precision. Uspensky's algorithm of Collins and Akritas, improved by Rouillier and Zimmermann and based on Descartes' rule of signs. This algorithms computes the real roots, isolated in intervals of arbitrary small width. It is implemented in Maple (functions fsolve and RootFinding[Isolate]). Software packages There are at least four software packages which can solve zero-dimensional systems automatically (by automatically, one means that no human intervention is needed between input and output, and thus that no knowledge of